Thermal Physics Kittel chapter 6 -- Entropy of mixing problem

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The discussion revolves around a challenging entropy of mixing problem from Kittel's Thermal Physics chapter 6, with the user struggling to derive the correct change in entropy formula (2Nlog(2)). The user has explored various papers for different approaches but remains stuck. A request for a clearer image of the user's work is made, emphasizing the need for better visibility. Additionally, tips for using LaTeX to post mathematical equations more effectively are offered. Clear communication and presentation of work are highlighted as essential for problem-solving in physics.
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Homework Statement
Suppose that a system of N atoms of type A is placed
in diffusive contact with a system of N atoms of type B at the same temperature
and volume. Show that after diffusive equilibrium is reached the total entropy
is increased by 2N log 2. The entropy increase 2N log 2 is known as the entropy
of mixing. If the atoms are identical (A = B), show that there is no increase in
entropy when diffusive contact is established. The difference in the results has
been called the Gibbs paradox.
Relevant Equations
sigma = log(g), mu = tau*log(N/V*n_Q), sigma = N[log(V*n_Q/N)+5/2]
I've been working on this problem for the past 3 days. I have other papers with different ways of tackling the problem. However, I just cannot get to the answer (change in entropy = 2Nlog(2)).
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Welcome to PF.

Your attached picture of your work is very light and hard to read. Can you upload a better image please?

Also, I will send you a message with tips for posting math equations at PF using LaTeX. That is a much better way to show your work in the future here. :smile:
 

Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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